topic: special products: square of a binomial
DESCRIPTION
Topic: Special Products: Square of a Binomial. Essential Question. How can special products and factors help determine patterns from various real-life situations?. Introduction. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Topic: Special Products: Square of a Binomial](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815b78550346895dc97435/html5/thumbnails/1.jpg)
Topic: Special Products: Square of a Binomial
![Page 2: Topic: Special Products: Square of a Binomial](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815b78550346895dc97435/html5/thumbnails/2.jpg)
Essential Question
How can special products and factors help determine patterns from various real-life situations?
![Page 3: Topic: Special Products: Square of a Binomial](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815b78550346895dc97435/html5/thumbnails/3.jpg)
Introduction Man cannot live without a smoother relationship with others. So that when two persons are related to each other, their relationship can be described in two opposite ways. If Dr. Rubio is John’s teacher, then we can also say that John is Dr. Rubio’s student. This is the same true in Algebra, numbers/expressions too are related to each other. We can also say that 4 is related to 2 in manner that 4 is the square of 2 and 2 is the square root of 4.
![Page 4: Topic: Special Products: Square of a Binomial](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815b78550346895dc97435/html5/thumbnails/4.jpg)
Special Products
In mathematics products are obtained by multiplication. In this section, you will discover patterns that help you determine the products of polynomials. These are called special products. They are called special products because products are obtained through definite patterns.
![Page 5: Topic: Special Products: Square of a Binomial](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815b78550346895dc97435/html5/thumbnails/5.jpg)
Recall: Laws of Exponents1. The Product of Powers
am ∙ an = am+n
Examples:
x3 ∙ x2 = x5
x4 ∙ x5 = x9
![Page 6: Topic: Special Products: Square of a Binomial](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815b78550346895dc97435/html5/thumbnails/6.jpg)
Another Example
(2x3) (-3x4) =
-6x7
![Page 7: Topic: Special Products: Square of a Binomial](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815b78550346895dc97435/html5/thumbnails/7.jpg)
2. The Power of a Power
(am)n = amn
Examples:(x4)3 = x12
(x2)3 = x6
(4x3)2 = 16x6
![Page 8: Topic: Special Products: Square of a Binomial](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815b78550346895dc97435/html5/thumbnails/8.jpg)
Another Example
(3y4z)5 =
243y20z5
![Page 9: Topic: Special Products: Square of a Binomial](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815b78550346895dc97435/html5/thumbnails/9.jpg)
3. The Power of a Product
(ab)m = ambm
Examples:(2x)3 = 8x3
(2a2b4c7)4 = 16a8b16c28
![Page 10: Topic: Special Products: Square of a Binomial](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815b78550346895dc97435/html5/thumbnails/10.jpg)
Another Example
(-5x4y5z)2 =
25x8y10z2
![Page 11: Topic: Special Products: Square of a Binomial](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815b78550346895dc97435/html5/thumbnails/11.jpg)
Square of a Binomial
(x+y)2
(x-y)2
![Page 12: Topic: Special Products: Square of a Binomial](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815b78550346895dc97435/html5/thumbnails/12.jpg)
Multiply. We can find a shortcut.
(x + y) (x + y)
x² + xy + xy + y2
= x² + 2xy + y2Shortcut: Square the first term, add twicethe product of both terms and add the square of the second term.
This is a “Perfect Square Trinomial.”
(x + y)2
This is the square of a binomial pattern.
![Page 13: Topic: Special Products: Square of a Binomial](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815b78550346895dc97435/html5/thumbnails/13.jpg)
Multiply. Use the shortcut.
(4x + 5)2
= (4x)² + 2(4x●5) + (5)2
Shortcut:
= 16x² + 40x + 25
x² + 2xy + y2
![Page 14: Topic: Special Products: Square of a Binomial](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815b78550346895dc97435/html5/thumbnails/14.jpg)
Try these!
(x + 3)2
(5m + 8)2
(2x + 4y)2
(-4x + 7)2
x² + 6x + 9
25m² + 80m + 64
4x² + 16xy + 16y²
16x²- 56x + 49
![Page 15: Topic: Special Products: Square of a Binomial](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815b78550346895dc97435/html5/thumbnails/15.jpg)
Multiply. We can find a shortcut.
(x – y) (x – y)
x² - xy - xy + y2
= x² - 2xy + y2
This is a “Perfect Square Trinomial.”
(x – y)2
This is the square of a binomial pattern.
![Page 16: Topic: Special Products: Square of a Binomial](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815b78550346895dc97435/html5/thumbnails/16.jpg)
Multiply. Use the shortcut.
(3x - 7)2
Shortcut:
= 9x² - 42x + 49
x² - 2xy + y2
![Page 17: Topic: Special Products: Square of a Binomial](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815b78550346895dc97435/html5/thumbnails/17.jpg)
Try these!
(x – 7)2
(3p - 4)2
(4x - 6y)2
x² - 14x + 49
9p² - 24p + 16
16x² - 48xy + 36y²
![Page 18: Topic: Special Products: Square of a Binomial](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815b78550346895dc97435/html5/thumbnails/18.jpg)
Homework # 2